To apply reflection ellipsometry to determine the real and imaginary parts of the refractive index of biological tissues simultaneously, we combine reflection ellipsometry with total internal reflection to warrant minimal influences by the strong scattering and absorption of biological tissues. A K9 glass prism with refractive index 1.51468 at wavelength $632.8\mathrm{nm}$ and a Glan prism polarizer with an angular sampling interval of $0.1°$ were used in our experimental setup. Using the setup, the complex refractive indices of some typical mammalian tissues were measured under the wavelength of $632.8\mathrm{nm}$ . The results show that the indices of porcine muscle, liver, pancreas, and dermis tissues were $1.3713+0.062i$ , $1.3791+0.0087i$ , $1.3517+0.0113i$ , and $1.3818+0.0049i$ , respectively.